...inscribed angle subtended by the difference of the opposite intercepted arcs. PROPOSITION XVII. THEOREM. The opposite angles of a quadrilateral inscribed in...a circle, are together equal to two right angles. The opposite angles A, C, or ABC, ADC, of the inscribed quadrilateral ABCD, are together equal to two...

...324', 6 = 137', с = 431', d = 122', then q = 44079-76 D'. SECTION XXXI. Рвов. All the sides of a quadrilateral, whose opposite angles are together equal to two right angles (about which, consequently, a circle may be described), are given: required to find its area. SOLUT....

...324', b = 137', с = 431х, d = 122х, then q = 44079-76 Dх. ' SECTION XXXI. PHOB. All the sides of a quadrilateral, whose opposite angles are together equal to two right angles (about which, consequently, a circle may be described), are given: required to ßnd us area. SOLUT....

...other given angle, to which it is external or internal, contrary to prop. 16, b. 1. PROP. 22. THEOR. The opposite angles of a quadrilateral inscribed in a circle, are together equal to two rig/it angles. For of either triangle, into which one of the diagonals resolves the quadrilateral,...

...which joins their centres, shall pass through the point of contact. 10. The opposite angles of any quadrilateral inscribed in a circle, are together equal to two right angles. 11. If a straight line touch a circle, and from the point of contact a straight line be drawn cutting...

...the difference of the angles BDE, ADE, will be invariable. SECTION III. 1. The opposite angles of Buy quadrilateral inscribed in a circle, are together equal to two right angles. No parallelogram can be inscribed in a circle, unless it be rectangular. 2. In equal circles the angles...

...the square on the other part. Deduce the same from the preceding propositions of the Second Book. 6. The opposite angles of a quadrilateral inscribed in...a circle, are together equal to two .right angles. Shew that no parallelogram, except a rectangle, can be inscribed in a circle. 7. If a straight line...

...will become Q=i&2 sec20 secsx t»n Q5 which is calculable by logarithms. 73. Given the four sides of a quadrilateral whose opposite angles are together equal to two right angles, to find the angles and the area. Let the sides AB, BC, CD, and DA, of the quadrilateral be represented...

...the squares of the lines joining the angular points with the middle points of the opposite sides. 12. The opposite angles of a quadrilateral inscribed in...a circle are together equal to two right angles. A segment of a circle rolls upon a plane from one end of its circumference to the other. Shew that the...

...square of half the line is equal to the square of the line made up of the half and the produced part. 3. The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles. o. If the opposite angles of a quadrilateral are together equal to two right angles, the quadrilateral...